Conditions For Existence Of Solutions Research Articles

A stationary free boundary problem modeling electrostatic MEMS

A free boundary problem describing small deformations in a membrane based model of electrostatically actuated MEMS is investigated. The existence of stationary solutions is established for small voltage values. A justification of the widely studied narrow-gap model is given by showing that steady state solutions of the free boundary problem converge toward stationary solutions of the narrow-gap model when the aspect ratio of the device tends to zero.

Existence of solutions for a class of boundary value problems of semilinear differential inclusions

In this paper, a class of boundary problems for second order semilinear differential inclusions is studied. By applying techniques from multivalued analysis and fixed point theorems due to Covitz–Nadler, Bohnenblust–Karlin and Schaefer, some existence results of solutions are presented for the nonlinear term which is a Lipschitz continuous, upper or lower semicontinuous multivalued map, respectively. As consequences some existence conditions of solutions are given for a class of second order semilinear differential systems.

Lyapunov-type least-squares problems over symmetric cones

The Lyapunov-type least-squares problem over symmetric cone is to find the least-squares solution of the Lyapunov equation with a constraint of symmetric cone in the Euclidean Jordan algebra, and it contains the Lyapunov-type least-squares problem over cone of semidefinite matrices as a special case. In this paper, we first give a detailed analysis for the image of Lyapunov operator in the Euclidean Jordan algebra. Relying on these properties together with some characterizations of symmetric cone, we then establish some necessary and⧹or sufficient conditions for solution existence of the Lyapunov-type least-squares problem. Finally, we study uniqueness of the least-squares solution.

Closed-loop MIMO transceiver with space-time multilayer transmit selection

A closed-loop multiple-input multiple-output (MIMO) transceiver combining space–time multilayer precoding and transmit selection is proposed. The transmitter design consists in optimizing the number of space–time transmit layers as well as the partitioning of the transmit antennas into the selected number of space–time layers. We show that this problem can be translated into jointly selecting, from a finite alphabet, two transmit matrices that define, respectively, the multilayer space–time code and the antenna mapping to be used. The parametrization of the proposed design takes into account all possible space–time layering schemes in between spatial multiplexing and transmit diversity for a fixed number of transmit antennas and linear precoder structure. Sufficient conditions for solution existence using a linear space–time zero forcing receiver are discussed. Simulation results compare the proposed transceiver with some MIMO schemes and corroborate the benefits of closed-loop multilayer selection in terms of capacity and bit error rates. Copyright © 2012 John Wiley & Sons, Ltd.

On the two-stage problem of linear stochastic programming with quantile criterion and discrete distribution of the random parameters

Consideration was given to the two-stage problem of stochastic linear programming with a discrete distribution of the random parameter vector. The property of continuity of the quantile function in strategy was proved, the sufficient conditions for existence of solution were formulated, and an algorithm to determine the guaranteeing solution was constructed on the basis of the confidence method and the duality theorem. A deterministic equivalent of the considered problem in the form of a linear programming problem was given for the scalar case.

Computation of initial conditions and inputs for given outputs of fractional and positive discrete-time linear systems

Computation of initial conditions and inputs for given outputs of fractional and positive discrete-time linear systemsThe problem of computation of initial conditions and inputs for given outputs of fractional standard and positive discrete-time linear systems is formulated and solved. Necessary and sufficient conditions for existence of solution to the problem are established. It is shown that there exist the unique solutions to the problem only if the pair (A, C) of the system is observable.

Exact Asymptotic Expansion of Singular Solutions for the (2 + 1)‐D Protter Problem

We study three‐dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in ℝ2. In contrast to the planar Darboux problem the three‐dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions. On the other hand, it is known that for smooth right‐hand side functions there is a uniquely determined generalized solution that may have a strong power‐type singularity at one boundary point. This singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone. The present paper describes asymptotic expansion of the generalized solutions in negative powers of the distance to this singular point. We derive necessary and sufficient conditions for existence of solutions with a fixed order of singularity and give a priori estimates for the singular solutions.

Analytical Study of Tangent Orbit and Conditions for Its Solution Existence

This paper presents an analytical study of the two-body tangent orbit technique by providing solution-existence conditions. The flight-direction angle is used to describe and solve this problem. Closed-form solutions are obtained for three classic problems: specified arrival flight-direction angle, specified departure flight-direction angle, and cotangent transfers. Not all of the problems admit solutions; thus, closed-form conditions for solution existence are provided by imposing a positive semilatus rectum constraint and a negative transfer-orbit energy (elliptic orbit transfer) constraint. The final solution-existence condition is then provided in terms of the true anomaly range for initial or final orbit. The singularity problem of 180 deg orbit transfer is also analyzed. Several examples are provided to verify the proposed analytical methods.

An iterative solution to coupled quaternion matrix equations

This note studies the iterative solution to the coupled quaternion matrix equations [?pi=1 T1i(Xi), ?pi=1 T2(Xi)... ?pi=1 Tp(Xi)] = [M1, M2,???, Mp], where Tsi,s = 1, 2,???, p; is a linear operator from Qmi,xni onto Qps?qs, Ms ? Qps?qs,s = 1, 2,???, p.i = 1, 2,???, p, by making use of a generalization of the classical complex conjugate graduate iterative algorithm. Based on the proposed iterative algorithm, the existence conditions of solution to the above coupled quaternion matrix equations can be determined. When the considered coupled quaternion matrix equations is consistent, it is proven by using a real inner product in quaternion space as a tool that a solution can be obtained within finite iterative steps for any initial quaternion matrices [X1(0),???,Xp (0)] in the absence of round-off errors and the least Frobenius norm solution can be derived by choosing a special kind of initial quaternion matrices. Furthermore, the optimal approximation solution to a given quaternion matrix can be derived. Finally, a numerical example is given to show the efficiency of the presented iterative method.

Stationary solutions for a generalized Kadomtsev-Petviashvili equation in bounded domain

In this work, we are mainly concerned with the existence of stationary solutions for the generalized Kadomtsev-Petviashvili equation in bounded domain in R n 8

Existence of solutions for perturbed abstract measure functional differential equations

In this article, we investigate existence of solutions for perturbed abstract measure functional differential equations. Based on the Arzela-Ascoli theorem and the fixed point theorem, we give sufficient conditions for existence of solutions for a class of perturbed abstract measure functional differential equations. Our system includes the systems studied in some previous articles as special cases and our sufficient conditions for existence of solutions are less conservative. An example is given to illustrate the effectiveness of our existence theorem of solutions.

Geometrically Nonlinear Analysis in the Vicinity of Critical Points by the Generalized Inverse

In the geometrically nonlinear analysis for equilibrium paths, the determinant of the tangent stiffness matrix at the critical point becomes zero so that a numerically unstable situation appears in the vicinity of critical points. To avoid such a situation, many numerical methods including the arc-length method and the perturbation method have been developed. In this paper, an analytical method to pursue the geometrically nonlinear equilibrium paths in the vicinity of critical points such as limit point and bifurcation point is presented by using the generalized inverse. In the first part, the perturbation equations for the incremental equilibrium equations are derived. Then, critical points on the equilibrium path are classified into limit point and bifurcation point by using the existence condition of solution. In the second part, an analytical method for post-critical paths beyond critical points is presented by means of the generalized inverse. In the final part, the application of the present method to the post-buckling analysis of a shallow arch and cable domes subjected to the symmetrical loads is shown.

Suffcient conditions for existence of solutions of a lower dimensional variational problem

Solutions of variational problems under ane boundary conditions can be viewed equivalently as solutions of an implicit differential equation coupled with another equation that relates to quasiaffinity on the quasiconvex envelope of the integrand. In this work we derive conditions on an integrand and on its quasiconvex envelope which are sufficient for existence of solutions of a related lower dimensional variational problem derived through a dimension reduction process.

Multiple stationary solutions of euler-poisson equations for non-isentropic gaseous stars

The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this paper is concerned with the existence of stationary solutions of Euler-Poisson equations for some velocity fields and entropy functions that solve the conservation of mass and energy. Under different restriction to the strength of velocity field, we get the existence and multiplicity of the stationary solutions of Euler-Poisson system.

Nonmonotone equilibrium problems: coercivity conditions and weak regularization

We consider a general equilibrium problem in a finite-dimensional space setting and propose a new coercivity condition for existence of solutions. We also show that it enables us to create a broad family of regularization methods with preserving well-definiteness and convergence of the iteration sequence without additional monotonicity assumptions. Some examples of applications are also given.

On stationary solutions of the Vlasov-Poisson equations

We study the existence of stationary solutions of the Vlasov-Poisson equations for x ∈ ℝN. We prove the absence of stationary solutions represented by Maxwell-Boltzmann distributions.

Risk Averse Members Coordination with Extended Buy-Back Contract

This paper considers how to coordinate a supply chain (SC) consisted of one supplier and one retailer who possess different risk aversion preference with a contract. Based on the classical buy-back contract, this paper presents an extended buy-back contract. In addition to the member’s objective of maximizing his expected profit, downside risk constraint is used to represent the SC member’s risk aversion preference. Under different risk aversion preference combination, the SC perfect solution existence conditions are identified and the specific contract is provided accordingly. This research finds out that, with a low risk aversion supplier and a high risk aversion retailer, the supplier as the SC coordinator can give the retailer incentive to increase the order quantity so as to reach SC perfect coordination. Finally a numerical analysis verifies the effectiveness of the extended buy-back contract.

On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions

The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in L1 is established for a class of stationary boundaryvalue problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming profile, are treated. The method is based on establishing the weak compactness of approximate solutions by using estimates of the entropy production.

푸리에 급수를 이용한 이족보행로봇의 보행 궤적 해석해 생성

This article describes a simple method for generating the walking trajectory for the biped humanoid robot. The method used a simple inverted model instead of complex multi-mass model and a reasonable explanation for the model simplification is included. The problem of gait trajectory generation is to find the solution from the desired ZMP trajectory to CoG trajectory. This article presents the analytic solution for the bipedal gait generation on the bases of ZMP trajectory. The presented ZMP trajectory has Fourier series form, which has finite or infinite summation of sine and cosine functions, and ZMP trajectory can be designed by calculating the coefficients. From the designed ZMP trajectory, this article focuses on how to find the CoG trajectory with analytical way from the simplified inverted pendulum model. Time segmentation based approach is adopted for generating the trajectories. The coefficients of the function should be designed to be continuous between the segments, and the solution is found by calculating the coefficients with this connectivity conditions. This article also has the proof and the condition of solution existence.

Global existence for a system of weakly coupled nonlinear Schrödinger equations

This paper discusses the weakly coupled nonlinear Schrodinger equations in the supercritical case. With the best constant of the Gagliardo-Nirenberg inequality, we derive a sufficient condition for the global existence of solutions; this condition is expressed in terms of stationary solutions (nonlinear ground state).